Approximate Solutions for Time-Fractional Fornberg–Whitham Equation with Variable Coefficients

Fractal and Fractional

article

Fahad Alsidrani¹  Adem Kılıçman²  Norazak Senu² 

[1] Department of Mathematics, College of Science and Arts, Qassim University;Institute for Mathematical Research, Universiti Putra Malaysia;Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia

关键词: fractional Fornberg–Whitham equation;    approximate solution;    partial differential equation;    Riemann–Liouville derivatives;    Caputo’s derivatives;    variational iteration method;    Adomian decomposition method;    homotopy analysis method;   

DOI  :  10.3390/fractalfract7030260

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

In this research, three numerical methods, namely the variational iteration method, the Adomian decomposition method, and the homotopy analysis method are considered to achieve an approximate solution for a third-order time-fractional partial differential Equation (TFPDE). The equation is obtained from the classical (FW) equation by replacing the integer-order time derivative with the Caputo fractional derivative of order η = ( 0 , 1 ] with variable coefficients. We consider homogeneous boundary conditions to find the approximate solutions for the bounded space variable l < χ < L and l , L ∈ R. To confirm the effectiveness of the proposed methods of non-integer orderη , the computation of two test problems was presented. A comparison is made between the obtained results of the (VIM), (ADM), and (HAM) through tables and graphs. The numerical results demonstrate the effectiveness of the three numerical methods.

【 授权许可】

CC BY